Notice: The reproducibility variables underlying each score are classified using an automated LLM-based pipeline, validated against a manually labeled dataset. LLM-based classification introduces uncertainty and potential bias; scores should be interpreted as estimates. Full accuracy metrics and methodology are described in [1].
An Online Convex Optimization Approach to Blackwell's Approachability
Authors: Nahum Shimkin
JMLR 2016 | Venue PDF | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Theoretical | In this paper we present a more direct formulation that relies on general Online Convex Optimization (OCO) algorithms, along with basic properties of the support function of convex sets. This leads to a general class of approachability algorithms, depending on the choice of the OCO algorithm and the used norms. Blackwell s original algorithm and its convergence are recovered when Follow The Leader (or a regularized version thereof) is used for the OCO algorithm. The paper also includes several proofs and lemmas (e.g., Proposition 3, Proposition 4, Lemma 6, Theorem 7, Proposition 12, Lemma 13, Proposition 14, Proposition 15, Lemma 16). |
| Researcher Affiliation | Academia | Nahum Shimkin EMAIL Faculty of Electrical Engineering Technion Israel Institute of Technology Haifa 32000, ISRAEL. The institution 'Technion Israel Institute of Technology' and the email domain 'ee.technion.ac.il' indicate an academic affiliation. |
| Pseudocode | Yes | Algorithm 1 (OCO-based Approachability Meta-Algorithm) Given: A closed, convex and approachable set S; a procedure (e.g., a linear program) to compute x (I), for a given vector w, so that (10) is satisfied; an OCO algorithm A for the functions ft(w) = w, rt + h S(w), with Regret T(A) a(T). Repeat for t = 1, 2, . . . : 1. Obtain wt from the OCO algorithm applied to the convex functions fk(w) = w, rk + hk(w), k t 1, so that inequality (11) is satisfied. 2. Choose xt according to (10), so that wt, r(xt, j) h S(wt) 0 holds for all j J. 3. Observe Nature s action jt, and set rt = r(xt, jt). |
| Open Source Code | No | The paper does not contain any explicit statements about releasing source code, nor does it provide links to a code repository. |
| Open Datasets | No | The paper is theoretical and focuses on algorithm design and proofs; it does not describe any experiments that would use datasets, nor does it provide access information for any. |
| Dataset Splits | No | The paper is theoretical and does not involve experiments with datasets, therefore, no dataset splits are provided. |
| Hardware Specification | No | The paper is theoretical and focuses on mathematical formulations and algorithms; it does not describe any experimental setup or specific hardware used for computations. |
| Software Dependencies | No | The paper describes theoretical algorithms and does not specify any particular software, libraries, or their version numbers used for implementation or experimentation. |
| Experiment Setup | No | The paper is theoretical and focuses on algorithm design and proofs, rather than empirical experiments. Therefore, it does not provide details on experimental setup, hyperparameters, or training configurations. |